Financial Toolbox

zero2disc

Discount curve given a zero curve

Syntax

• [DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates, Settle, 
  InputCompounding, InputBasis)
  

Arguments

ZeroRates	A number of bonds (NUMBONDS) by 1 vector of annualized zero rates, as decimal fractions. In aggregate, the rates constitute an implied zero curve for the investment horizon represented by CurveDates.
CurveDates	A NUMBONDS-by-1 vector of maturity dates (as serial date numbers) that correspond to the zero rates.
Settle	A serial date number that is the common settlement date for the zero rates; i.e., the settlement date for the bonds from which the zero curve was bootstrapped.
InputCompounding	(Optional) A scalar that indicates the compounding frequency per year used for annualizing the input zero rates in ZeroRates. Allowed values are:
	1	annual compounding
	2	semi-annual compounding (default)
	3	compounding three times per year
	4	quarterly compounding
	6	bimonthly compounding
	12	monthly compounding
	365	daily compounding
	-1	continuous compounding
InputBasis	(Optional) Input day-count basis used for annualizing the input zero rates. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.

Description

[DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates, Settle, InputCompounding, InputBasis) returns a discount curve given a zero curve and its maturity dates.

DiscRates	A NUMBONDS-by-1 vector of discount factors, as decimal fractions. In aggregate, the factors in constitute a discount curve for the investment horizon represented by CurveDates.
CurveDates	A NUMBONDS-by-1 vector of maturity dates (as serial date numbers) that correspond to the discount rates. This vector is the same as the input vector CurveDates.

Examples

Given a zero curve over a set of maturity dates and a settlement date

• ZeroRates = [0.0464
               0.0509
               0.0524
               0.0525
               0.0531
               0.0525
               0.0530
               0.0531
               0.0549
               0.0536];
  
  CurveDates = [datenum('06-Nov-2000')
                datenum('11-Dec-2000')
                datenum('15-Jan-2001')
                datenum('05-Feb-2001')
                datenum('04-Mar-2001')
                datenum('02-Apr-2001')
                datenum('30-Apr-2001')
                datenum('25-Jun-2001')
                datenum('04-Sep-2001')
                datenum('12-Nov-2001')];
  
  Settle = datenum('03-Nov-2000');
  

The zero curve was compounded daily on an actual/365 basis.

• InputCompounding = 365;
  InputBasis = 3;
  

Execute the function

• [DiscRates, CurveDates] = zero2disc(ZeroRates, CurveDates,... 
  Settle, InputCompounding, InputBasis)
  

which returns the discount curve DiscRates at the maturity dates CurveDates.

• DiscRates =
  
        0.9996
        0.9947
        0.9896
        0.9866
        0.9826
        0.9787
        0.9745
        0.9665
        0.9552
        0.9466
  
  CurveDates =
  
        730796
        730831
        730866
        730887
        730914
        730943
        730971
        731027
        731098
        731167
  

For readability, ZeroRates and DiscRates are shown here only to the basis point. However, MATLAB computed them at full precision. If you enter ZeroRates as shown, DiscRates may differ due to rounding.

See Also

disc2zero and other functions for Term Structure of Interest Rates

zbtyield

zero2fwd